Metrics
Andriy Koval
Tuesday, June 24, 2014
Mapping Church Attendance in Time
Cross-Sectional View
The focal variable of interest is attend, the item measuring church attendance for the year that preceded the interview date. The questionnaire recorded the responses on the ordinal scale.
Creating frequency distributions for each of the measurement wave we have:
Here, missing values are used in the calculation of total responses to show the natural attrition in the study. Assuming that attrition is not significantly associated with the outcome measure, we can remove missing values from the calculation of the total and look at prevalence of response endorsements over time.
Tracing the rate of change of prevalence in a line graph, we see more clearly which categores increase over time (e.g. “Never”), which decline (e.g. “”About once/week), and which stay relatively stable (e.g. “About twice/month”)
Inspecting the prevalence trajectories across races. 
Source: local data frame [40 x 7]
Groups: sampleF, yearF, raceF
sampleF yearF raceF attendF count total percent
1 Cross-Sectional 2000 Black Never 170 967 0.175801
2 Cross-Sectional 2000 Black Once or Twice 204 967 0.210962
3 Cross-Sectional 2000 Black Less than once/month 144 967 0.148914
4 Cross-Sectional 2000 Black About once/month 59 967 0.061013
5 Cross-Sectional 2000 Black About twice/month 74 967 0.076525
6 Cross-Sectional 2000 Black About once/week 197 967 0.203723
7 Cross-Sectional 2000 Black Several times/week 109 967 0.112720
8 Cross-Sectional 2000 Black Everyday 10 967 0.010341
9 Cross-Sectional 2000 Hispanic Never 187 812 0.230296
10 Cross-Sectional 2000 Hispanic Once or Twice 216 812 0.266010
11 Cross-Sectional 2000 Hispanic Less than once/month 123 812 0.151478
12 Cross-Sectional 2000 Hispanic About once/month 49 812 0.060345
13 Cross-Sectional 2000 Hispanic About twice/month 43 812 0.052956
14 Cross-Sectional 2000 Hispanic About once/week 131 812 0.161330
15 Cross-Sectional 2000 Hispanic Several times/week 57 812 0.070197
16 Cross-Sectional 2000 Hispanic Everyday 6 812 0.007389
17 Cross-Sectional 2000 Non-B/Non-H Never 1201 4159 0.288771
18 Cross-Sectional 2000 Non-B/Non-H Once or Twice 870 4159 0.209185
19 Cross-Sectional 2000 Non-B/Non-H Less than once/month 498 4159 0.119740
20 Cross-Sectional 2000 Non-B/Non-H About once/month 252 4159 0.060591
21 Cross-Sectional 2000 Non-B/Non-H About twice/month 268 4159 0.064439
22 Cross-Sectional 2000 Non-B/Non-H About once/week 757 4159 0.182015
23 Cross-Sectional 2000 Non-B/Non-H Several times/week 293 4159 0.070450
24 Cross-Sectional 2000 Non-B/Non-H Everyday 20 4159 0.004809
25 Oversample 2000 Black Never 231 1143 0.202100
26 Oversample 2000 Black Once or Twice 246 1143 0.215223
27 Oversample 2000 Black Less than once/month 158 1143 0.138233
28 Oversample 2000 Black About once/month 91 1143 0.079615
29 Oversample 2000 Black About twice/month 78 1143 0.068241
30 Oversample 2000 Black About once/week 232 1143 0.202975
31 Oversample 2000 Black Several times/week 94 1143 0.082240
32 Oversample 2000 Black Everyday 13 1143 0.011374
33 Oversample 2000 Hispanic Never 210 859 0.244470
34 Oversample 2000 Hispanic Once or Twice 220 859 0.256112
35 Oversample 2000 Hispanic Less than once/month 123 859 0.143190
36 Oversample 2000 Hispanic About once/month 52 859 0.060536
37 Oversample 2000 Hispanic About twice/month 47 859 0.054715
38 Oversample 2000 Hispanic About once/week 143 859 0.166473
39 Oversample 2000 Hispanic Several times/week 60 859 0.069849
40 Oversample 2000 Hispanic Everyday 4 859 0.004657
Longitudinal View
Graphs above shows change in the cross-sectional distribution of responses over the years. Modeling the change in these response frequencies is handled well by Markov models. LCM, however, works with longitudinal data, modeling the trajectory of each individual and treating attendance as a continuous outcome.
To demonstrate mapping of individual trajectories to time, let’s select a dataset that would include personal identifyer (id), cohort indicator (byear), wave of measurement (year) and the focal variable of interest - worship attendance (attend).
ds<- dsL %>% dplyr::filter(year %in% c(2000:2011), id==47) %>%
dplyr:: select(id, byear, year, attend, attendF)
print(ds) id byear year attend attendF
1 47 1982 2000 5 About twice/month
2 47 1982 2001 2 Once or Twice
3 47 1982 2002 4 About once/month
4 47 1982 2003 2 Once or Twice
5 47 1982 2004 3 Less than once/month
6 47 1982 2005 2 Once or Twice
7 47 1982 2006 2 Once or Twice
8 47 1982 2007 3 Less than once/month
9 47 1982 2008 2 Once or Twice
10 47 1982 2009 1 Never
11 47 1982 2010 1 Never
12 47 1982 2011 1 NeverThe view above lists attendance data for subjust with id = 47. Mapping his attendance to time we have
where vertical dimension maps the outcome value and the horizontal maps the time. There will be a trajecory for each of the
length(unique(dsL$id))[1] 8983subjects in total. Unless specified otherwise, only individuals from the cross-sample will be used in the model to increase external validity.
ds<- dsL %>% dplyr::filter(sample==1)Each of such trajectories imply a story, a life scenario. Why one person grows in his religious involvement, while other declines, or never develops an interest in the first place? To demostrate how interpretations of trajectories can vary among individuals consider the following scenario.
Attendance trajectories of subjects with ids 4, 25, 35, and 47 are plotted in the next graph
The respondent id=35 reported attending no worship services in any of the years, while respodent id=25 seemed to frequent it, indicating weekly attendance in 8 out of the 12 years. Individual id=47 started as a fairly regular attendee of religious services in 2000 (5= “about twice a month”), then gradually declined his involvement to nill in 2009 and on. Respondent id=4, on the other hand started off with a rather passive involvement, reporting attended church only “Once or twice” in 2000, maintained a low level of participation throughout the years, only to surge his attendance in 2011. Latent curve models will describe intraindividual trajectories of change, while summarizinig the interindividual similarities and trends.
Previous research in religiousity indicated that age might be one of the primary factors explaining interindividual differences in church attendance. To examine the role of age, we change the metric of time from waves of measurement, as in the previous graph, to biological age. There are, however, a number of ways information about age was recorded.
ds<- dsL %>% dplyr::filter(id %in% c(4,25,35,47),year %in% c(2000:2011)) %>%
dplyr::select(idF,attend, year, byear, ageyear, agemon, ageyear) %>%
mutate(time=year-2000, age=(year-byear+1), ageCurrent = agemon/12)
print(ds[ds$idF==25,]) idF attend year byear ageyear agemon time age ageCurrent
13 25 5 2000 1983 17 214 0 18 17.83
14 25 7 2001 1983 18 226 1 19 18.83
15 25 7 2002 1983 19 236 2 20 19.67
16 25 2 2003 1983 21 254 3 21 21.17
17 25 7 2004 1983 21 261 4 22 21.75
18 25 5 2005 1983 22 272 5 23 22.67
19 25 7 2006 1983 23 284 6 24 23.67
20 25 5 2007 1983 24 295 7 25 24.58
21 25 7 2008 1983 25 307 8 26 25.58
22 25 7 2009 1983 26 319 9 27 26.58
23 25 7 2010 1983 27 332 10 28 27.67
24 25 7 2011 1983 28 342 11 29 28.50ds idF attend year byear ageyear agemon time age ageCurrent
1 4 2 2000 1981 19 238 0 20 19.83
2 4 1 2001 1981 20 251 1 21 20.92
3 4 3 2002 1981 21 262 2 22 21.83
4 4 1 2003 1981 22 276 3 23 23.00
5 4 2 2004 1981 23 287 4 24 23.92
6 4 2 2005 1981 24 297 5 25 24.75
7 4 2 2006 1981 25 309 6 26 25.75
8 4 2 2007 1981 26 320 7 27 26.67
9 4 2 2008 1981 27 336 8 28 28.00
10 4 1 2009 1981 28 344 9 29 28.67
11 4 2 2010 1981 29 357 10 30 29.75
12 4 5 2011 1981 30 368 11 31 30.67
13 25 5 2000 1983 17 214 0 18 17.83
14 25 7 2001 1983 18 226 1 19 18.83
15 25 7 2002 1983 19 236 2 20 19.67
16 25 2 2003 1983 21 254 3 21 21.17
17 25 7 2004 1983 21 261 4 22 21.75
18 25 5 2005 1983 22 272 5 23 22.67
19 25 7 2006 1983 23 284 6 24 23.67
20 25 5 2007 1983 24 295 7 25 24.58
21 25 7 2008 1983 25 307 8 26 25.58
22 25 7 2009 1983 26 319 9 27 26.58
23 25 7 2010 1983 27 332 10 28 27.67
24 25 7 2011 1983 28 342 11 29 28.50
25 35 1 2000 1983 17 216 0 18 18.00
26 35 1 2001 1983 18 227 1 19 18.92
27 35 1 2002 1983 19 239 2 20 19.92
28 35 1 2003 1983 20 250 3 21 20.83
29 35 1 2004 1983 21 264 4 22 22.00
30 35 1 2005 1983 22 274 5 23 22.83
31 35 1 2006 1983 23 286 6 24 23.83
32 35 1 2007 1983 24 297 7 25 24.75
33 35 1 2008 1983 25 310 8 26 25.83
34 35 1 2009 1983 26 320 9 27 26.67
35 35 1 2010 1983 27 334 10 28 27.83
36 35 1 2011 1983 28 345 11 29 28.75
37 47 5 2000 1982 18 220 0 19 18.33
38 47 2 2001 1982 19 233 1 20 19.42
39 47 4 2002 1982 20 243 2 21 20.25
40 47 2 2003 1982 21 257 3 22 21.42
41 47 3 2004 1982 22 266 4 23 22.17
42 47 2 2005 1982 23 280 5 24 23.33
43 47 2 2006 1982 24 292 6 25 24.33
44 47 3 2007 1982 25 302 7 26 25.17
45 47 2 2008 1982 26 315 8 27 26.25
46 47 1 2009 1982 27 326 9 28 27.17
47 47 1 2010 1982 28 339 10 29 28.25
48 47 1 2011 1982 29 351 11 30 29.25Note that for person id = 25 the age was recorded as 21 years for both 2003 and 2004. However, when you examine age in months (agemon) you can see this is rounding issue that disappears once a more precise scale is used. To avoid this potentially confusing peculiarity, age in years will be either calculated as (age = year - byear + 1)
Plotting age, caclulated as age = year - byear + 1 
ds<- dsL %>% dplyr::filter(id %in% c(4,25,35,47),year %in% c(2000:2011)) %>%
dplyr::select(idF,year,attend,agemon,ageyear) %>%
mutate(time=year-2000, age=ageyear)
head(ds,12) idF year attend agemon ageyear time age
1 4 2000 2 238 19 0 19
2 4 2001 1 251 20 1 20
3 4 2002 3 262 21 2 21
4 4 2003 1 276 22 3 22
5 4 2004 2 287 23 4 23
6 4 2005 2 297 24 5 24
7 4 2006 2 309 25 6 25
8 4 2007 2 320 26 7 26
9 4 2008 2 336 27 8 27
10 4 2009 1 344 28 9 28
11 4 2010 2 357 29 10 29
12 4 2011 5 368 30 11 30Plotting age, caclulated as age = ageyear 
Plotting age, caclulated as age = agemon/12
ds<- dsL %>% dplyr::filter(id %in% c(4,25,35,47),year %in% c(2000:2011)) %>%
dplyr::select(idF,year,attend,agemon,ageyear,byear) %>%
mutate(time=year-2000, age=agemon/12)
head(ds,12) idF year attend agemon ageyear byear time age
1 4 2000 2 238 19 1981 0 19.83
2 4 2001 1 251 20 1981 1 20.92
3 4 2002 3 262 21 1981 2 21.83
4 4 2003 1 276 22 1981 3 23.00
5 4 2004 2 287 23 1981 4 23.92
6 4 2005 2 297 24 1981 5 24.75
7 4 2006 2 309 25 1981 6 25.75
8 4 2007 2 320 26 1981 7 26.67
9 4 2008 2 336 27 1981 8 28.00
10 4 2009 1 344 28 1981 9 28.67
11 4 2010 2 357 29 1981 10 29.75
12 4 2011 5 368 30 1981 11 30.67